Whatever cock-up claims could be made about Tuesday's string of ministerial walkouts, the resignation of Hazel Blears yesterday was an unmistakable act of revenge against the prime minister. Coming from the cabinet minister in charge of local government, it was also a display of contempt for her own party on the eve of today's county council and European elections. With Labour already expected to suffer its worst results since the first world war, Blears's decision to jump before the expected reshuffle can only be seen as an attempt to destabilise the government still further in preparation for a decisive push to force Gordon Brown out.

That the latest round of resignations started with the former Blairite health secretary Patricia Hewitt – who has landed lucrative contracts with Alliance Boots and Cinven, a major private healthcare company, on the back of her previous job – and ended up with Blears, the Blairite minister with one of the most outrageous expenses records in government, gives a pretty clear idea of both the politics and ethics of the source of the latest onslaught. As one Downing Street insider said yesterday, Blears's "disgraceful behaviour" may have even "solidified the Labour party – for now".

But not for long. There is bound to be a move against Brown in the coming days, at least from the Labour backbenches, where MPs are already drumming up support for a no-confidence letter aimed at pushing the cabinet to act. Everything depends on the numbers. But the fact that the plotters are discussing a truncated leadership election timetable which would cut out hundreds of thousands of affiliated union members from voting – exactly the kind of people New Labour has so disastrously lost touch with – underlines the political agenda of the planned putsch.

In fact, Labour's rules already allow the cabinet, in consultation with the national executive, to pick a new party leader when in government if he or she "for whatever reason, becomes permanently unavailable" until an election can be held. But whether a majority can be assembled in cabinet right now to move against Brown – or whose interests it would serve – is another matter.

The prime minister seems likely to try to bind the most powerful Blairites even closer to him in the reshuffle to shore up his defences. The current expectation is that Peter Mandelson will be given a souped-up version of his existing job, as supremo of the national business ­recovery plan; and it hardly seems in David Miliband's interests to back a coup set to derail his own leadership ambitions in favour of Alan Johnson.

Brown is, of course, a ditherer and a half-measures merchant who bears a heavy responsibility for New Labour's fateful embrace of the City and ­corporate excess — he's still at it in his self-­defeating backing for part-privatisation of Royal Mail — and struggles to connect with his colleagues, let alone the public. But it's also the case that his government has begun to inch in a more progressive direction since the crash of last autumn: moving to take control of the banks, boosting spending to offset the impact of recession and finally beginning to raise taxes for the wealthy.

So for Labour to oust him now because of the public backlash over the MPs' expenses scandal, which has engulfed all the main parties and is lapping at the front door of David ­Cameron's second home, looks at least premature. The Labour case for Alan Johnson, favourite to succeed Brown, would be to minimise the scale of expected defeat at the general election, perhaps underpinned by his commitment to a referendum on electoral reform.

That might be a stronger argument later in the year, though it assumes a popularity that isn't yet tested. But the pressure for an early general election in the case of a Johnson succession now would be overwhelming; the contest would be clouded by expenses referendums and likely to deliver a Labour meltdown. Why should turkeys, in this case Labour MPs, vote for Christmas? If Brown is replaced, "we'd have to call an immediate election and be decimated", one cabinet minister told me yesterday. "This is a perfect storm and we will get through it." Yes, Brown was a poor communicator, but "if you have to choose between ability to govern and communicate, governing is more important".

The test of that will come in the next few days. But in any case, New Labour's decomposition long predates the froth of expenses scams. It is rooted in the profound deceit of the Iraq war, the party's embrace of unfettered corporate power and greed and its abandonment of core supporters – which have in turn paved the way for Cameron's Tories.

Yet while as in the rest of the Europe, the door has also been opened to the racist right, the kind of political ­challenge to neoliberalism that has mushroomed in Germany, France and the Netherlands is still almost entirely absent in Britain: the product of a ­prostrate left and the stifling combination of the electoral system and Labour's abandonment of internal democracy. Both in the economy and politics, this is a New Labour crisis to which there is no New Labour solution.

But it does provide the opportunity for MPs and others to negotiate a change of direction, whether over control of the banks, ID cards or postal privatisation – against which the government faces a huge backbench revolt and is already haggling with MPs and trade unionists. Meanwhile, in what seems like a throwback to 19th-century politics, Esther Rantzen, newly crowned queen of the political independents, has been speculating that the clearout of corrupt MPs was a chance to bring in a cohort of "distinguished doctors" or "well thought-of teachers". But as the GMB union leader Paul Kenny counters, it should be a "fantastic opportunity" to bring in 30 or 40 working-class MPs, who are in much shorter supply.

The events of the past couple of days have familiar echoes of last year's abortive attempt to oust Brown in favour of David Miliband, though the government's position is certainly now even weaker. Brown's vacillations with the Blairite irreconcilables, who are determined keep Labour tethered to neoliberalism and break with the unions, has got him nowhere. He should have sacked Blears weeks ago. The ­challenge is now not simply whether Brown or Johnson should be leader, but to move beyond the failed politics of New Labour altogether.